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Just as an introduction for SDP-partners, this is a

Just as an introduction for SDP-partners, this is a. theoretical ppt on properties of triangles in which first, 3 properties are formulated and visualised (recalling or introducing new concepts) afterwards, 2 of these properties are proved.

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Just as an introduction for SDP-partners, this is a

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  1. Just as an introduction for SDP-partners, this is a • theoretical ppt on properties of triangles • in which • first, 3 properties are formulated and visualised • (recalling or introducing new concepts) • afterwards, 2 of these properties are proved • while building up the proves interactively, • pupils draw and write on prefab-sheets which • combine multiple slides into 1 page (sheets are • included here but not translated)

  2. 7.3 Properties of triangles

  3. 1) A A middle parallel of a triangle (a line connecting the middles of two sides of the triangle) C B is // with the third side and has half of its length

  4. 2 1 2) Two medians of a triangle (lines through angle and middle of opposite side) A divide each other in 2 parts which are in the ratio of 2 to 1 C B

  5. x y h 3) A In a rectangular triangle the height onto the hypothenuse is middleproportional C B between the line segments h2 = x . y in which it divides the hypothenuse

  6. A C B Een middenparallel van een driehoek (een lijnstuk dat de ……………………………………………………………… …………………………..) is // met de derde zijde en ……………………………. • Gegeven: ABC met M het midden van [AB] en N het midden van [BC] • Te bewijzen: MN // AC en …………………... • Bewijs: • Beschouw  ABC en  MBN : • B = ………………….. • = ……… (……………..)   ABC …………………… • M = A • AB wordt door MN en AC gesneden • volgens ……………………………….. ……………………………… • …………………… |MN| = ………………     

  7. |MN| = |AC| 1) 2) A middle parallel of a triangle (a line which ………………………………………………………… is // with the third side ……………… connects the middles of two sides of the triangle) and has half of its length A Given: ABC with M the middle of [AB] and N the middle of [BC] To be proved: MN // AC and …………………... M C B N

  8. A M C B N   ABC …………. • Prove: • Consider  ABC and  MBN : • = …………………..  in common (……….) 2   MBN 1)

  9. A M C B N  ABC ………….   MBN 1)  AB is cut by MN and AC according to ……………………………….. equal corresponding angles  MN // AC

  10. A M C B N |MN| = |AC|  ABC ………….   MBN 2) = 2  = 2 

  11. In een rechthoekige driehoek is de hoogte op de schuine zijde ………….…………………………………. tussen de lijnstukken waarin ze de schuine zijde verdeelt. (zie p A.18) • Gegeven: rechthoekige  ABC met BH de hoogetlijn op [AC] • Te bewijzen:|BH|2 = |AH|.|HC| • Bewijs: • Beschouw  AHB en  BHC : • A = …………………………………... • C = …………………………………... (……….)   AHB …………………… A C B    ……………………….. of ………………………..

  12. In a rectangular triangle the heigth onto the hypothenuse is ………….………… between the line segments in which it divides the hypothenuse middleproportional Given: rectangular  ABC with BH the perpendicular onto [AC] To be proven: …………….. A H |BH|2 = |AH|.|HC| C B

  13. 1 2 (angle angle)   AHB   |BH|2 = |AH|.|HC| A Prove: Consider  AHB and  BHC : Name the angles in B: H C B    BHC

  14. … and now exercises …

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